What three numbers have an average of 263?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 263. This means if we add these three numbers together and divide by 3, we should get 263.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 263 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 263 * 3 = x + y + z
- So, the sum of our three numbers should be: 789
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 789.
Solution 1:
263, 263, 263
Verification:
(263 + 263 + 263) / 3 = 789 / 3 ≈ 263
This solution is correct!
Solution 2:
263, 263, 263
Verification:
(263 + 263 + 263) / 3 = 789 / 3 ≈ 263
This solution is correct!
Solution 3:
327, 19, 443
Verification:
(327 + 19 + 443) / 3 = 789 / 3 ≈ 263
This solution is correct!
Solution 4:
497, 54, 238
Verification:
(497 + 54 + 238) / 3 = 789 / 3 ≈ 263
This solution is correct!
Solution 5:
274, 302, 213
Verification:
(274 + 302 + 213) / 3 = 789 / 3 ≈ 263
This solution is correct!
Explanation:
As you can see, there are many possible solutions. We can find more by:
- Choosing any two numbers
- Subtracting their sum from 789 to get the third number
Remember:
- The numbers don't have to be whole numbers.
- They can even be negative (although that might not make sense in some real-world contexts).
- The order of the numbers doesn't matter for the average.